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\project{5: Galois Theory}{Weeks 1-10}

\textbf{\'Evariste Galois} embodied the proverb ``The flame that burns twice as bright burns half as long.''  He died at twenty in a duel surrounding a broken love affair, and in the night before (knowing he would likely lose) wrote a letter outlining several mathematical ideas that were called ``the most substantial piece of writing in the whole literature of mankind.''

His work was the first to use the word group in its modern sense; with it, he created the entire field of Galois theory, which allowed mathematicians to disprove (amongst other things) a longstanding conjecture that all roots of polynomials can be expressed in terms of a finite number of radicals and elementary operations.

In this project, you will be Galois.  (Minus the ``dying tragically in a duel'' part.)  Namely, you will work your way through his results, prove and study his theorems, and recreate as many of his results as you can!  A successful run of this project will consist of a group creating a collection of presentations/writeups that would take a first-year CCS mathematics student through the mathematical highlights of Galois theory.


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